An Expected Value Analysis of When to Avoid Type 1 and Type 2 Statistical Errors in Applied Research

Abstract

For decades, applied researchers have relied heavily on either the null hypothesis significance testing procedure (NHSTP) or Bayesian statistics to help them determine the probability of the null hypothesis given their findings. While there may be some flaws in both methods, there are cases where the probability of the null hypothesis can be known, or at least estimated fairly accurately, thus making such analyses worthwhile. Assuming the worth of using such analyses, another issue in play is whether or not to avoid Type 1 or Type 2 statistical errors. While much has been said about the importance of avoiding both types of errors, we offer a new way of looking at the situation. We use an Expected Value analysis to help applied researchers determine when to avoid either type of error. We give examples and perform simulations to back up our mathematical arguments. Theoretical and applied issues are discussed.